# The side of the square is 18 cm. The perimeter of the rectangle is equal to the perimeter of the square.

**The side of the square is 18 cm. The perimeter of the rectangle is equal to the perimeter of the square. The length of the rectangle is 1/2 of its width, and the width is 24 cm. How many square centimeters is the area of the square larger than the area of the rectangle?**

1. Calculate the length of the second side of the rectangle:

24 x 1/2 = 12 centimeters.

2. We calculate the perimeter (P) of the square, taking into account that all sides of this geometric figure

are equal:

18 x 4 = 72 centimeters.

3. Calculate the area (S) of the square:

S = 18 x 18 = 324 centimeters².

4. Calculate the area (S) of the rectangle:

12 x 24 = 288 centimeters².

5. Calculate the difference between the areas of a square and a rectangle:

324 – 288 = 36 centimeters².

Answer: the difference between the areas of a square and a rectangle is 36 centimeters².